Example 10 - Example of rotor connected by a rigid mechanical coupling with parallel misalignment.

In this example, we use a finite element (FE) model to represent the rotor that is available as a test rig in LMest - UFU for demonstrating the results obtained when we have a misalignment defect present in the system. The system is composed of a flexible steel shaft with \(0.914 m\) length and \(0.019 m\) diameter (it is modeled using Timoshenko beam-element), two rigid discs (both of steel with \(0.150 m\) diameter and \(0.020 m\) thickness) and two self alignment ball bearings. A model updating procedure was used to obtain a representative FE model for the numerical simulations presented in this work. In this sense, a heuristic optimization technique (Differential Evolution) was used to determine the unknown parameters of the model, namely the stiffness and damping coefficients of the bearings, besides the proportional damping.

import numpy as np

import ross as rs
from ross.defects import *
from ross.defects.misalignment import misalignment_flex_parallel_example

"""Create example rotor with given number of elements."""
steel2 = rs.Material(name="Steel", rho=7850, E=2.17e11, G_s=81.2e9)
#  Rotor with 6 DoFs, with internal damping, with 10 shaft elements, 2 disks and 2 bearings.
i_d = 0
o_d = 0.019
n = 33

# fmt: off
L = np.array(
        [0  ,  25,  64, 104, 124, 143, 175, 207, 239, 271,
         303, 335, 345, 355, 380, 408, 436, 466, 496, 526,
         556, 586, 614, 647, 657, 667, 702, 737, 772, 807,
         842, 862, 881, 914]
         )/ 1000
# fmt: on

L = [L[i] - L[i - 1] for i in range(1, len(L))]

shaft_elem = [
    rs.ShaftElement6DoF(
        material=steel2,
        L=l,
        idl=i_d,
        odl=o_d,
        idr=i_d,
        odr=o_d,
        alpha=8.0501,
        beta=1.0e-5,
        rotary_inertia=True,
        shear_effects=True,
    )
    for l in L
]

Id = 0.003844540885417
Ip = 0.007513248437500

disk0 = rs.DiskElement6DoF(n=12, m=2.6375, Id=Id, Ip=Ip)
disk1 = rs.DiskElement6DoF(n=24, m=2.6375, Id=Id, Ip=Ip)

kxx1 = 4.40e5
kyy1 = 4.6114e5
kzz = 0
cxx1 = 27.4
cyy1 = 2.505
czz = 0
kxx2 = 9.50e5
kyy2 = 1.09e8
cxx2 = 50.4
cyy2 = 100.4553

bearing0 = rs.BearingElement6DoF(
    n=4, kxx=kxx1, kyy=kyy1, cxx=cxx1, cyy=cyy1, kzz=kzz, czz=czz
)
bearing1 = rs.BearingElement6DoF(
    n=31, kxx=kxx2, kyy=kyy2, cxx=cxx2, cyy=cyy2, kzz=kzz, czz=czz
)

rotor = rs.Rotor(shaft_elem, [disk0, disk1], [bearing0, bearing1])

"""Inserting a mass and phase unbalance and defining the local response."""
massunbt = np.array([5e-4, 0])
phaseunbt = np.array([-np.pi / 2, 0])
probe1 = (14, 0)
probe2 = (22, 0)

"""Calculate the response of the rotor connected by a rigid mechanical coupling with parallel misalignment."""
misalignment = rotor.run_misalignment(
    coupling="rigid",
    dt=0.0001,
    tI=0,
    tF=5,
    eCOUP=2e-4,
    TD=0,
    TL=0,
    n1=0,
    speed=1200,
    massunb=massunbt,
    phaseunb=phaseunbt,
    print_progress = False,
)

"""Plots the time response for the two given probes."""
results = misalignment.run_time_response()
results.plot_1d([probe1, probe2]).show()

"""Plots the frequency response for the two given probes."""
misalignment.plot_dfft([probe1, probe2], range_freq=[0, 100], yaxis_type="log").show()